The Most Common Inferential Statistics and When to Use Them

Descriptive and inferential statistics are the two broad categories in the statistics field. Whereas descriptive statistics summarizes the characteristics of a given data set, inferential statistics help to make predictions and draw conclusions based on sample data. In need of statistical analysis? We offer both inferential and descriptive statistics services at affordable rates and help you to draw valid conclusions and make correct predictions for your project. To draw valid conclusions and make correct predictions in an inferential statistics study, one must understand what inferential statistics are and when to use them.

In inferential data analysis, one uses sample data to make inferences about the entire population from which the sample was drawn. The purpose of inferential statistics is to estimate population parameters and test hypotheses to draw conclusions from a sample and generalize the findings to the whole population. To achieve this purpose, it is fundamental to ascertain whether one has the ideal representative sample for the target population.

The sampling methods used to select and recruit the study participants determine how representative the sample is of the entire population. Random sampling methods are recommended when determining representative samples to reduce the effects of human bias and prevent sampling errors. This article contains a detailed discussion of the most common inferential statistics and when to use them.

Choosing a Representative Sample for the Entire Population

To generalize results obtained from a sample to the entire population, one must ensure that the sample reflects the characteristics of the population from which it was drawn. This can be achieved by defining the study population, choosing a random sample, and using a statistical analysis method that incorporates sampling errors. Only the correct sample size can yield accurate results in hypothesis testing or when estimating population parameters. Inferential statistics are used to draw inferences or conclusions when the required extent of data analysis is beyond describing a sample's characteristics or summarizing data.

Standard Tools for Inferential Analysis

The inferential analysis uses tools such as confidence intervals, hypothesis tests, and regression analysis. Although inferential statistics tools may produce descriptive statistics such as the mean and standard deviation, one should understand how to correctly use them to make inferences or draw conclusions according to the specific research aims and objectives.

(1). Confidence intervals

A confidence interval uses a range of values within which the actual population values are likely to fall by incorporating uncertainty and sample error. Confidence intervals use the variability around a statistic to create interval estimates for a particular population parameter. Each confidence interval is associated with a confidence level that tells the odds of the interval containing the parameter estimate if one repeats the study.

(2). Hypothesis tests

A hypothesis test is used to assess associations or relationships between variables using sample data and comparing populations or two or more groups. Statistical tests are used to test hypotheses while estimating sampling errors to draw conclusions or make valid inferences. A statistical test can be parametric or non-parametric.

Parametric tests operate under various assumptions. These include:

• The population values from which the sample data was drawn follow a normal distribution.
• There is a similarity between the variances and the measure of the speed of each of the comparison groups.
• The available sample data sufficiently represents the entire population.

If the collected data does not comply with the assumptions, one should use distribution-free or non-parametric tests. Non-parametric tests do not operate under the assumption of a normal distribution of values. Statistical tests fall under three categories: Correlation tests, regression analysis, and tests of comparison. An inferential statistics example used to compare two or more groups is the t-test statistic. Correlation test examples include Pearson's r, Spearman's r, and Chi-square, which are used to find the extent of association between two variables. Regression tests demonstrate whether changes in predictor variables have an impact on the outcome variable.

(3). Regression analysis

The regression model of analysis is used to describe the relationship between a dependent variable and a set of independent variables. The analysis incorporates appropriate hypothesis tests that assist in determining whether the relationships observed in representative samples exist in the larger population. Whether to use simple linear regression, multiple linear regression, nominal, ordinal, or logistic regression depends on the number and types of variables involved in the study. Regression analysis can be used in a real-life situation to determine the relationship between heart attack (the outcome variable) and body weight and lifestyle (predictor variables).

How to Estimate Population Parameters Using Sample Statistics

Statistics and parameters are the numbers used to describe the characteristics of a sample and a population. A sample statistic, such as a mean or sample standard deviation, describes the sample, while a parameter, such as the population mean or population standard deviation, describes the whole population. The most common estimates a researcher can make about a population are interval and point estimates. A point estimate is a parameter's single value estimate, while an interval estimate provides a range of values within which the parameter is expected to lie. Both estimates are essential for clearly determining where a population parameter should lie.

Common Types of Inferential Statistics and When to Calculate Them

To draw a valid conclusion about an entire population using sample data, it is fundamental to understand the different types of inferential statistics and when to calculate each of them. The common types of inferential statistics include:

(1). T-tests

A t-test is a statistical test that can be used to compare means. The common types of t-tests include one-sample t-tests, independent samples t-tests, and paired/dependent samples t-tests. To calculate any type of t-test statistic, one should find the difference between the means and divide it by a variation measure. The t-test tells the statistical significance of the mean differences. An instance when t-tests can be calculated is when a researcher wants to know whether administering a new drug for leukemia can significantly increase a patient’s life expectancy by comparing treatment and control groups. One can calculate a t-test to determine whether the findings are generalizable to the entire population living with leukemia.

(i). One-sample t-test

In a one-sample t-test, one is interested in one data set or one mean, and the population's mean to which one intends to compare the calculated mean is known. One-sample t-tests are used when comparing sample data to the mean of a known population.

(ii)Independent-samples t-tests

An independent-sample t-test can be used when comparing data from two separate and unrelated samples. In this test, one is interested in comparing two separate groups or non-overlapping data sets. Different study participants or sources were involved when collecting the data.

(iii). Dependent-samples t-test

Paired/dependent samples t-test is used when comparing data from the same people or related groups over time, especially in a pre-test and post-test setting.

(2). Analysis of Variance (ANOVA)

ANOVA is a statistical method used when finding and analyzing significant differences between means. Whereas the t-test is used to compare only two means at a time, ANOVA can compare multiple means at the same time or the effects of various factors on a single measure. Types of ANOVA include one-way ANOVA, repeated measures/within-groups ANOVA, and factorial ANOVA. For instance, if a researcher wants to determine whether the level of education is the same for athletes, one could survey members from football, basketball, and netball associations. ANOVA can be used to determine whether there is a difference in the mean education level among the athletes.

(a). One-way ANOVA

One can compare three or more groups/levels along the same dimension with one-way ANOVA. The researcher/scholar is interested in comparing three or more separate, non-overlapping data sets or groups.

(b). Repeated measures ANOVA

A repeated measures ANOVA compares data from the same people or related groups over time, especially in longitudinal studies that involve tracking the same people over a given period. The separate data sets must have been derived from the same population over time to obtain accurate and reliable results with repeated measures of ANOVA.

(c). Factorial ANOVA

Factorial ANOVA is used in cases where the researcher/scholar wants to compare the means of two or more variables, dimensions, or factors. Because there are more than two groups/factors being compared, follow-up tests may be required for further interpretation of the results.

(3). Correlation analysis

Correlations are used to determine the strength of the relationship or association between two variables. Correlation analysis is mostly used when testing relationships between categorical or quantitative variables. Our professional statisticians utilize correlation analysis to determine the strength of the association between eating junk foods and weight gain or people’s level of education and the type of vegetables they consume.

Differences Between Descriptive and Inferential Statistics

With the extensive expertise our professional statisticians possess, they easily differentiate the descriptive and inferential statistics to ensure the analysis conducted is accurate and also to clarify to our clients what analysis they have conducted. The main differences between descriptive and inferential statistics include:

1. Inferential statistics are used when drawing inferences and conclusions about a population by applying analytical tools to sample data. In contrast, descriptive statistics summarize and quantify the characteristics of the sample data.
2. The standard analysis tools for inferential statistics include regression analysis and hypothesis testing, while in descriptive statistics, measures of central tendency, frequency distribution, and measures of dispersion are used to summarize data.
3. Inferential statistics are used when inferring about an unknown population, while descriptive statistics help in describing a known sample or population data.
4. Among other measures, inferential statistics use the t-test, z-test, f-test, ANOVA, correlation, and regression, while descriptive statistics use the mean, median, variance, standard deviation, and mode.

The procedure for conducting inferential statistics includes sample selection, application of tools such as hypothesis tests, and making inferences or drawing statistical conclusions. A random sample must be selected to prevent sampling error. Logical reasoning is required to derive valid results and interpret them correctly in inferential analyses. After collecting data, one should determine the appropriate analysis to conduct to achieve the research objectives and answer specified questions.

Our expert statisticians have a wide knowledge of statistical analysis and always get the most out of your data to achieve meaningful insights. Contact us today to get customized solutions for your analysis, whether descriptive or inferential data analysis. We are available 24/7 to respond to your inquiries and clarifications. Chat with us now and request a free quote.